Non linear second order ode’s with missing independent variable \(x\). Reference this
Number of problems in this table is 297
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{3} y^{\prime \prime }+4 = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.193 |
|
|
\[ {}x^{\prime \prime } = \frac {k^{2}}{x^{2}} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
6.692 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime } \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
7.569 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.811 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
8.321 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.574 |
|
|
\[ {}y^{\prime \prime } = y y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.718 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.652 |
|
|
\[ {}y^{\prime \prime }+2 {y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.163 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.354 |
|
|
\[ {}y y^{\prime \prime }+1 = {y^{\prime }}^{2} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
13.393 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime } \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
4.402 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.67 |
|
|
\[ {}y^{\prime \prime }+2 {y^{\prime }}^{2} = 2 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
5.403 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.674 |
|
|
\[ {}\left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2} \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.127 |
|
|
\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
75.174 |
|
|
\[ {}y^{\prime \prime } = y^{3} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.783 |
|
|
\[ {}y y^{\prime \prime }-y^{2} y^{\prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
4.486 |
|
|
\[ {}y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.063 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime } \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
55.114 |
|
|
\[ {}2 y y^{\prime \prime } = y^{3}+2 {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
1.688 |
|
|
\[ {}y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
19.906 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.794 |
|
|
\[ {}y^{\prime \prime } = 2 y y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.987 |
|
|
\[ {}y^{3} y^{\prime \prime } = k \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.782 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2}-1 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
8.385 |
|
|
\[ {}\left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2} \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.61 |
|
|
\[ {}r^{\prime \prime } = -\frac {k}{r^{2}} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.896 |
|
|
\[ {}y^{\prime \prime } = \frac {3 k y^{2}}{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
14.666 |
|
|
\[ {}y^{\prime \prime } = 2 k y^{3} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.368 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
4.184 |
|
|
\[ {}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
8.885 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
2.019 |
|
|
\[ {}y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.004 |
|
|
\[ {}\left (y+1\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.104 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y} \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.116 |
|
|
\[ {}y^{\prime \prime } = 2 y y^{\prime } \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.908 |
|
|
\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
63.523 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right )^{3} = a^{2} {y^{\prime \prime }}^{2} \] |
2 |
4 |
4 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.842 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.884 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.857 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.142 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.98 |
|
|
\[ {}2 y y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.604 |
|
|
\[ {}{y^{\prime \prime }}^{2} = k^{2} \left (1+{y^{\prime }}^{2}\right ) \] |
2 |
4 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.845 |
|
|
\[ {}k = \frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{\frac {3}{2}}} \] |
2 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
✓ |
1.687 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.543 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.531 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 2 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.636 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.648 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.191 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.63 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.932 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-\cos \left (y\right ) y^{\prime }+y y^{\prime } \sin \left (y\right )\right ) \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
3.074 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right ) \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.854 |
|
|
\[ {}2 \left (y+1\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.474 |
|
|
\[ {}x x^{\prime \prime }-{x^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.963 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.32 |
|
|
\[ {}y y^{\prime \prime }+4 {y^{\prime }}^{2} = 0 \] |
1 |
5 |
6 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
4.504 |
|
|
\[ {}y^{\prime \prime } = y y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.777 |
|
|
\[ {}y^{\prime \prime } = -\frac {1}{2 {y^{\prime }}^{2}} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
8.194 |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
51.869 |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
133.487 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.132 |
|
|
\[ {}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.38 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.647 |
|
|
\[ {}y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
5.231 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
4.645 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.93 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
9.789 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.014 |
|
|
\[ {}y y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.801 |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.572 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.438 |
|
|
\[ {}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.994 |
|
|
\[ {}\left (y+1\right ) y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.032 |
|
|
\[ {}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.347 |
|
|
\[ {}y^{\prime \prime } = 2 y {y^{\prime }}^{3} \] |
1 |
3 |
4 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
142.67 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.911 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.004 |
|
|
\[ {}y^{\prime \prime } = -{\mathrm e}^{-2 y} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
63.49 |
|
|
\[ {}y^{\prime \prime } = -{\mathrm e}^{-2 y} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
62.529 |
|
|
\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
10.706 |
|
|
\[ {}2 y^{\prime \prime } = \sin \left (2 y\right ) \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
6.464 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.48 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-y y^{\prime } \cos \left (y\right )\right ) \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
5.556 |
|
|
\[ {}\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.111 |
|
|
\[ {}\left (y y^{\prime \prime }+1+{y^{\prime }}^{2}\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3} \] |
2 |
4 |
7 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
11.033 |
|
|
\[ {}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1 \] |
1 |
3 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
8.366 |
|
|
\[ {}4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3 \] |
1 |
4 |
4 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.635 |
|
|
\[ {}y y^{\prime \prime } = 1 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
0.869 |
|
|
\[ {}3 y y^{\prime \prime }+y = 5 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.069 |
|
|
\[ {}a y y^{\prime \prime }+b y = c \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.901 |
|
|
\[ {}a y^{2} y^{\prime \prime }+b y^{2} = c \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.931 |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.299 |
|
|
\[ {}y^{\prime \prime } = A y^{\frac {2}{3}} \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.175 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{y} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.547 |
|
|
\[ {}{y^{\prime \prime }}^{2} = 0 \] |
2 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.779 |
|
|
\[ {}{y^{\prime \prime }}^{n} = 0 \] |
0 |
2 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.619 |
|
|
\[ {}a {y^{\prime \prime }}^{2} = 0 \] |
2 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.717 |
|
|
\[ {}a {y^{\prime \prime }}^{n} = 0 \] |
0 |
2 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.572 |
|
|
\[ {}{y^{\prime \prime }}^{2} = 1 \] |
2 |
2 |
2 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.793 |
|
|
\[ {}{y^{\prime \prime }}^{3} = 0 \] |
3 |
1 |
1 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.933 |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = 0 \] |
2 |
6 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
7.969 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.861 |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = 1 \] |
2 |
6 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
10.206 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.548 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+y = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.526 |
|
|
\[ {}y {y^{\prime \prime }}^{2}+y^{\prime } = 0 \] |
2 |
12 |
8 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
66.283 |
|
|
\[ {}y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3} = 0 \] |
2 |
1 |
5 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
13.249 |
|
|
\[ {}y^{2} {y^{\prime \prime }}^{2}+y^{\prime } = 0 \] |
2 |
6 |
8 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
6.76 |
|
|
\[ {}y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2} = 0 \] |
4 |
12 |
52 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
51.904 |
|
|
\[ {}y^{3} {y^{\prime \prime }}^{2}+y y^{\prime } = 0 \] |
2 |
6 |
8 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.56 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.328 |
|
|
\[ {}y {y^{\prime \prime }}^{3}+y^{3} y^{\prime } = 0 \] |
3 |
1 |
5 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
9.137 |
|
|
\[ {}y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5} = 0 \] |
3 |
1 |
5 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
14.752 |
|
|
\[ {}y^{\prime \prime } y^{\prime }+y^{2} = 0 \] |
1 |
3 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.796 |
|
|
\[ {}y^{\prime \prime } y^{\prime }+y^{n} = 0 \] |
1 |
3 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.171 |
|
|
\[ {}y^{\prime \prime }-y^{2} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.3 |
|
|
\[ {}y^{\prime \prime }-6 y^{2} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.651 |
|
|
\[ {}y^{\prime \prime }-6 y^{2}+4 y = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.329 |
|
|
\[ {}y^{\prime \prime }-a y^{3} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.924 |
|
|
\[ {}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
68.896 |
|
|
\[ {}y^{\prime \prime }+6 a^{10} y^{11}-y = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
39.587 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{y} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.605 |
|
|
\[ {}y^{\prime \prime }+a \sin \left (y\right ) = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.068 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.406 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }-y^{\frac {3}{2}}+12 y = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
1.02 |
|
|
\[ {}y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.483 |
|
|
\[ {}y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.484 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.894 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.676 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime }-y^{3} = 0 \] |
1 |
3 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
6.498 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime }-y^{3}+a y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.935 |
|
|
\[ {}y^{\prime \prime }+\left (y+3 a \right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y = 0 \] |
1 |
0 |
3 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
1.095 |
|
|
\[ {}y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.779 |
|
|
\[ {}y^{\prime \prime }-2 a y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.697 |
|
|
\[ {}y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
18.211 |
|
|
\[ {}y^{\prime \prime }+a {y^{\prime }}^{2}+b y = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b y^{\prime }+c y = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
3.27 |
|
|
\[ {}y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.451 |
|
|
\[ {}y^{\prime \prime }+a {y^{\prime }}^{2}+b \sin \left (y\right ) = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
8.279 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
1.54 |
|
|
\[ {}y^{\prime \prime }+a y {y^{\prime }}^{2}+b y = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
0.865 |
|
|
\[ {}y^{\prime \prime }+a y \left (1+{y^{\prime }}^{2}\right )^{2} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
5.75 |
|
|
\[ {}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.01 |
|
|
\[ {}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b \] |
2 |
2 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
194.412 |
|
|
\[ {}y^{\prime \prime } = a \sqrt {{y^{\prime }}^{2}+b y^{2}} \] |
2 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
12.945 |
|
|
\[ {}y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.207 |
|
|
\[ {}y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = 0 \] |
2 |
2 |
4 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
6.375 |
|
|
\[ {}y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0 \] |
2 |
2 |
5 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
15.044 |
|
|
\[ {}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.146 |
|
|
\[ {}a y^{\prime \prime }+h \left (y^{\prime }\right )+c y = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.671 |
|
|
\[ {}y y^{\prime \prime }-a = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.039 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}-a = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
4.072 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.237 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.772 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.089 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} \ln \left (y\right ) = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.711 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.473 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+b y^{3} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.585 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 y^{2} a^{2}-2 b^{2} y^{3}+a y = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
1.108 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (y+1\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
2.427 |
|
|
\[ {}y y^{\prime \prime }-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.593 |
|
|
\[ {}y y^{\prime \prime }-a {y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.01 |
|
|
\[ {}y y^{\prime \prime }+a \left (1+{y^{\prime }}^{2}\right ) = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
5.073 |
|
|
\[ {}y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{3} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.191 |
|
|
\[ {}y y^{\prime \prime }+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
1.409 |
|
|
\[ {}y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
3.517 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = 0 \] |
2 |
2 |
4 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
6.839 |
|
|
\[ {}2 y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
4 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.296 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+a = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.714 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.088 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.093 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.28 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}-3 y^{4} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.87 |
|
|
\[ {}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.977 |
|
|
\[ {}2 y y^{\prime \prime }-3 {y^{\prime }}^{2}-4 y^{2} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.038 |
|
|
\[ {}2 y y^{\prime \prime }-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.665 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) = 0 \] |
1 |
1 |
5 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.901 |
|
|
\[ {}2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
11.312 |
|
|
\[ {}3 y y^{\prime \prime }-5 {y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.968 |
|
|
\[ {}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+4 y = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.537 |
|
|
\[ {}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
3.859 |
|
|
\[ {}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.375 |
|
|
\[ {}4 y y^{\prime \prime }-5 {y^{\prime }}^{2}+a y^{2} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.512 |
|
|
\[ {}12 y y^{\prime \prime }-15 {y^{\prime }}^{2}+8 y^{3} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.827 |
|
|
\[ {}n y y^{\prime \prime }-\left (n -1\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.852 |
|
|
\[ {}a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
6.141 |
|
|
\[ {}\left (a y+b \right ) y^{\prime \prime }+c {y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.493 |
|
|
\[ {}y^{2} y^{\prime \prime }-a = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.557 |
|
|
\[ {}\left (1+y^{2}\right ) y^{\prime \prime }+\left (1-2 y\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.92 |
|
|
\[ {}\left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.019 |
|
|
\[ {}a y \left (y-1\right ) y^{\prime \prime }-\left (a -1\right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
63.229 |
|
|
\[ {}a b y \left (y-1\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
48.549 |
|
|
\[ {}y^{3} y^{\prime \prime }-a = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.622 |
|
|
\[ {}y \left (1+y^{2}\right ) y^{\prime \prime }+\left (1-3 y^{2}\right ) {y^{\prime }}^{2} = 0 \] |
1 |
2 |
5 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.546 |
|
|
\[ {}2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
5.548 |
|
|
\[ {}\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
4 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
11.477 |
|
|
\[ {}\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
4 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✗ |
1887.566 |
|
|
\[ {}\left (y^{2}-1\right ) \left (y^{2} a^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-y^{2} a^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 y^{2} a^{2}\right ) y {y^{\prime }}^{2} = 0 \] |
1 |
1 |
0 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
14.163 |
|
|
\[ {}\sqrt {y}\, y^{\prime \prime }-a = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.237 |
|
|
\[ {}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.244 |
|
|
\[ {}\left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
48.585 |
|
|
\[ {}\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime }+y^{3} = 0 \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.789 |
|
|
\[ {}\left (y^{2} a^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0 \] |
2 |
6 |
6 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
3.497 |
|
|
\[ {}\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0 \] |
2 |
0 |
4 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
20.473 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.53 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.733 |
|
|
\[ {}2 y^{\prime \prime } = {\mathrm e}^{y} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.118 |
|
|
\[ {}y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.545 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.786 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.943 |
|
|
\[ {}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.129 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.327 |
|
|
\[ {}y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.143 |
|
|
\[ {}x^{3} x^{\prime \prime }+1 = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.418 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.799 |
|
|
\[ {}y^{\prime \prime } = 3 \sqrt {y} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
38.673 |
|
|
\[ {}y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2} \] |
2 |
2 |
4 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.189 |
|
|
\[ {}m x^{\prime \prime } = f \left (x^{\prime }\right ) \] |
0 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.896 |
|
|
\[ {}y^{\prime \prime } = 2 y^{3} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.053 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime } \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.69 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.668 |
|
|
\[ {}y y^{\prime \prime } = 1 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
0.632 |
|
|
\[ {}\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.163 |
|
|
\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
1.533 |
|
|
\[ {}y^{\prime \prime } = \frac {a}{y^{3}} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.326 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.005 |
|
|
\[ {}{y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2} \] |
2 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.263 |
|
|
\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
1.049 |
|
|
\[ {}y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.893 |
|
|
\[ {}x^{\prime \prime }+x-x^{3} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.03 |
|
|
\[ {}x^{\prime \prime }+x+x^{3} = 0 \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.734 |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x-x^{3} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.488 |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x+x^{3} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.491 |
|
|
\[ {}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
85.822 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.208 |
|
|
\[ {}y^{\prime \prime } y^{\prime } = 1 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
2.463 |
|
|
\[ {}y y^{\prime \prime } = -{y^{\prime }}^{2} \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.296 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime } \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.372 |
|
|
\[ {}\left (y-3\right ) y^{\prime \prime } = 2 {y^{\prime }}^{2} \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.821 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.182 |
|
|
\[ {}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.884 |
|
|
\[ {}\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.275 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 2 y y^{\prime } \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.186 |
|
|
\[ {}y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2} = 0 \] |
1 |
3 |
5 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
602.552 |
|
|
\[ {}y^{\prime \prime } y^{\prime } = 1 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
1.559 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime } \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.233 |
|
|
\[ {}y y^{\prime \prime } = 2 {y^{\prime }}^{2} \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.989 |
|
|
\[ {}\left (y-3\right ) y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.092 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.553 |
|
|
\[ {}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.678 |
|
|
\[ {}y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.701 |
|
|
\[ {}y^{\prime \prime } = -y^{\prime } {\mathrm e}^{-y} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.977 |
|
|
\[ {}y^{\prime \prime } = 2 y y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.579 |
|
|
\[ {}y^{\prime \prime } = 2 y y^{\prime } \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.012 |
|
|
\[ {}y^{\prime \prime } = 2 y y^{\prime } \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.766 |
|
|
\[ {}y^{\prime \prime } = 2 y y^{\prime } \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.308 |
|
|
\[ {}\left (y+1\right ) y^{\prime \prime } = {y^{\prime }}^{3} \] |
1 |
1 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.027 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.581 |
|
|
\[ {}2 y y^{\prime \prime }+y^{2} = {y^{\prime }}^{2} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
8.819 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.329 |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.97 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
6.869 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.484 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.346 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.649 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.721 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+y^{\prime }} \] |
2 |
3 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.595 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right ) \] |
0 |
1 |
1 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.464 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.342 |
|
|
\[ {}3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
2 |
3 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.937 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2} \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.493 |
|
|
\[ {}y^{\prime \prime } = 2 y y^{\prime } \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.768 |
|
|
\[ {}3 y^{\prime \prime } y^{\prime } = 2 y \] |
1 |
3 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.805 |
|
|
\[ {}2 y^{\prime \prime } = 3 y^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
4.26 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.703 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime } \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.682 |
|
|
\[ {}y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.768 |
|
|
\[ {}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.599 |
|
|
\[ {}y^{3} y^{\prime \prime } = -1 \] |
1 |
1 |
0 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
0.992 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime } \] |
1 |
1 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.674 |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{2 y} \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
71.557 |
|
|
\[ {}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2} \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.588 |
|
|
\[ {}x^{\prime \prime }+{x^{\prime }}^{2}+x = 0 \] |
1 |
2 |
2 |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.035 |
|
|
\[ {}x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.378 |
|
|
\[ {}x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0 \] |
0 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
0.585 |
|
|
\[ {}x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.542 |
|
|
\[ {}x^{\prime \prime }+x {x^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.524 |
|
|
\[ {}x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.703 |
|
|
\[ {}x^{\prime \prime }-x^{\prime }+x-x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.385 |
|
|
\[ {}y y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
8.125 |
|
|
|
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|
|
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|
|